Saturday, November 22, 2014

Sooner is Not Better, and There Is No "Best Feedback" (Post 5 of 10)

At the start of this series, I highlighted four claims about feedback that I thought were both widely heralded and wrong.
  1. Oral feedback is always better than written feedback.
  2. When it comes to feedback, the more the better!
  3. When it comes to feedback, the sooner the better!
  4. Feedback is all about helping students understand the mistakes they've made.
Since then, I've shared a case when I gave oral feedback and a case when I gave written feedback. In one case I gave lots of feedback and in the other I gave rather little feedback. 

Sometimes oral feedback is better than written feedback. Sometimes it's the other way around.

The point isn't just that these myths are wrong, though they are. It's that this talk of "best practices" (or "best activities") is such a limited and unhelpful way of talking about teaching. 

In this post I'll argue that sooner isn't always better. Then, it's time to put these sorts of claims to rest. There's a better way to talk about teaching.

Point: When It Comes To Feedback, The Sooner The Better

"In most cases, the sooner I get feedback, the better." (Seven Keys To Effective Feedback)

"Of course, it's not always possible to provide students with feedback right on the spot, but sooner is definitely better than later." (5 Research-Based Tips For Providing Students With Meaningful Feedback)

Counter-Point: Nah

A few weeks ago I gave a quiz to my geometry classes. We were at the end of a unit on quadrilateral properties and proofs, which was the area that my quiz targeted.

When looking at the quiz, I noticed that my three "always/sometimes/never" questions had gotten a huge variety of responses: "always, always, sometimes"; "sometimes, sometimes, it depends"; "sometimes, always, never", etc. 

A closer look confirmed that their thinking was all over the place. A handful of kids indicated that parallelograms have a line of symmetry. Others didn't recall that a kite can be split into two congruent triangles. Others thought that a trapezoid's diagonal divides it into two congruent triangles. Some proofs were nice, others needed lots of improvement. 

I quickly decided to give my class feedback and time to revise: no other activity that I could run in class would be able to address each individual mistake and give each student a chance to think about their specific area of need. 

I decided to wait a week. 

Why wait? It wasn't because I didn't have time. I think that waiting was the right decision. Consider the work of one of my students, Jake:

Jake showed some major limitations in his thinking on this quiz. Jake indicated that only parallelograms can be split along their diagonals to form two congruent triangles and that the consecutive angles of a parallelogram don't sum to 180 degrees. 

Jake was hard-working during class, and he participated actively in many of our conversations in class about parallelograms. In short, he hadn't slacked during the past two weeks. Despite this, he was still having trouble putting the pieces together. Would feedback help him where two weeks of instruction couldn't?

Maybe. But here's another thing I knew: the upcoming week quite possibly would help. Why? The unit we were beginning was studying how one shape (e.g. a parallelogram) can be dissected and rearranged to form a new shape (e.g. a rectangle). The activities that I was planning on running would give us a chance to physically rearrange shapes into other shapes. I thought that these activities would probably give me a number of great opportunities to address some of Jake's misconceptions about congruent triangles in kites and parallelograms. Or, at least, we could draw on these dissection examples when discussing his quiz when I did give Jake feedback.

Another factor: Jake was hard-working, but I saw a drop in engagement after a few days of "always, sometimes, never"-style questions. I wasn't shocked. We had been working on them for a few days, and questions that are posed in a similar fashion can start to bleed together after some time. I thought that Jake (and others) needed a break from these sorts of questions.

So I waited a week, and I gave feedback. And it was fine. 

OK, Great. Every Rule Has Exceptions. Including "The Sooner the Better." Who Cares?

Thanks for the question, sub-heading!

It's true: there are certainly times when the decision to wait a week to give feedback is the wrong one. And is that the majority of situations? The vast majority?

I don't know. I do know that there are lots of situations like my quadrilaterals quiz, and there are a lot of students like Jake. And that "the sooner the better!" is, strictly speaking, false. 

Here's the only question worth asking, then: do we learn much from a slogan like "the sooner the better"?

I don't think so. 

We don't need "5 Research-Proven Teaching Techniques" or "7 Activities For Learning" or "12 Qualities of Excellent Feedback." Ultimately, the work of teaching comes down to the decisions that we make, and writing about teaching should be about improving those decisions. 

What we do need is to talk about the dilemmas that we teachers commonly face, and try to find guidelines that help us make wise decisions in those scenarios.

Talk of "the sooner the better" isn't anywhere close to that. In the rest of this series, I'll try to talk more productively about decisions we face when giving feedback for revision. The stories that I've shared so far are my attempt at a start to that work.

This is the fifth post in a series on feedback. To read the rest of the posts click here.

Saturday, November 15, 2014

Against the Feedback Menu (Post 4 of 10)

So you're giving a presentation to teachers. It's called "Giving Effective Feedback to Students." You've got slides. You've got an audience. You've got 60 minutes.

How do you spend it?

The way we teachers talk about feedback, you're likely to present about the menu of options that teachers have for giving feedback. You'll talk about written vs. oral feedback; positive vs. negative feedback; individual vs. whole-class; timely vs. delayed feedback; lengthy vs. brief feedback; feedback for learning vs. feedback for evaluation.

That's certainly what's going on in Types of Feedback and Their Purposes:

Here's an opinion about how we talk about feedback: this is an insane way to talk about feedback.

What makes this crazy is the extraordinarily high level of abstraction. It's so high-level that it's practically philosophical: "What is good?", "How should we write?", "What's best to do?"

In a different planet, we would talk about teaching situations and how to improve them. That seems more sensible to me than talking about things that improve learning and then matching them to various scenarios, post-hoc.

By analogy, imagine that I was presenting on "Giving Effective Drugs to Patients" instead of "Giving Effective Feedback to Students."

My first slide would, of course, cite a relevant research table showing -- conclusively! -- that giving drugs helps patient outcomes.

Of course, first we would have to define "drugs." (The first sign that we're dealing at too high a level of abstraction -- we don't even know what we're talking about!) 

Too many doctors just prescribe Asprin for everything, don't you find? (Compare to: "Feedback vs. Advice".

Now, time to dig into the details! Doctors have to make important decisions about the amount of drugs, as well as the timing.

And don't forget - no two patients are the same!

My point here is not to compare teaching to medicine. They're very different fields! I'm making a more limited analogy between the way we talk about instructional techniques and the way doctors talk about medical strategies.

"What is the most effective way to use drugs?" is an incredibly general question, and not a particularly helpful one. A better question to ask would start with the ailments: "What's the most effective way to treat whooping cough?" or whatever.

So too in math education. The "menu of options" style of presentation is pervasive in talk about teaching, but it doesn't have to be. A more productive route, I think, would be to start thinking about various specific teaching-scenarios that are common throughout the profession. How do we make good teaching decisions in these scenarios?

What sorts of scenarios am I talking about? Here are two that I'm spinning off of earlier posts in this series.
  • Toni's Fixed Mindset: How do you help a talented student who is socially unable to admit to any mathematical limitations to learn a complex skill, like proof? (Post #3)
  • Misinterpreting Bar Graphs: How do you best help a class that has a wide variety of minor, but significant misconceptions that can't be addressed all it once through whole-class instruction? (Post #2)
In the case of Toni, I argued that the best feedback was whole-class, oral instruction that lead to students choosing just one solution to revise. In the case of the bar graphs, I argued for giving individual "highlight"-style feedback and group-time to revise the entire assignment.

Written vs. Oral? Whole-class vs. Individual? Immediate vs. Delayed?

How much good can come of these questions?


This is the fourth post in a series on feedback. To read the rest of the posts click here.

Tuesday, November 11, 2014

Letter to A "Second Drafts" Skeptic (3 of 10)

Dear Michael,

I read your previous post and was intrigued by your argument. I'm sympathetic to the idea that "giving feedback" is hopelessly vague. And, I agree: giving feedback is only sometimes effective.

You suggested that teachers need to take the energy they put into "giving feedback" and redirect it into "facilitating second drafts."

I'm skeptical.

I'll grant that your post showed an example of "second drafting" that led to student learning. Sure. But who says that "improving the classwork" is ever the most effective activity to get to this learning? After all, the effectiveness of a teaching technique is at least partly determined by how much time it takes. Also: maybe you got lucky? Maybe asking students to improve their work wasn't the right decision to make, even if it happened to lead to learning.

In short, you've got more work to do.




Dear Skeptic,

I agree completely. Here’s what I’ll try do to address these concerns. First, I’ll argue that there are at least some situations when helping students improve their classwork is the right instructional decision. But it’s a long way from saying that “second drafting” sometimes works to saying that it works in most classrooms, in many situations. I won’t be able to bridge that gap entirely, but I'll try to get as close as I can.

To start, I want to tell you about an awesome student of mine, Toni.

Toni is a 9th Grader. She's new to our school, and she stood out early on. On the first day of class, I gave students a version of the handshake problem and put them in groups. Toni took a quick look at the problem and said, "Oh this is simple" to her groupmates. She took a marker and whiteboard and scribbled a few calcuations without a word of explanation to the folks she was working with. She quickly and accurately calculated how many handshakes we’d need to all shake hands (but didn’t try the second half of the problem in search of a generalization) and sat back and called me over.

"We're finished." 

It was only after I nudged them that Toni (and her group) really dug into the second problem.

This is the sort of student Toni is. Quick, accurate, sharp, and likes being quick, accurate and sharp.

Toni has a group of friends in class that she gets along well with. One day I overheard them talking about how smart they were at math. Toni said, "Oh yeah I'm really good at math. It's in my blood." Being good at math is clearly an important part of Toni's identity. She sees smartness in math as something pre-determined and relatively fixed.

Another thing about Toni: she often didn’t justify her work, even when the assignment explicitly called for justification. In her classwork or quizzes, Toni would quickly come to conclusions that were poorly justified. Often (usually) they were dead-on. But sometimes they weren’t. For instance, for several days Toni was absolutely sure that she had found a counter-example to SAS.

I tried to give Toni some one-on-one feedback on her SAS counter-example during classwork. It was hard going. She didn’t seem interested in what I had to say, was easily distracted. I tried to get her to use reasoning to check her conclusion, but her confidence seemed absolute.

This pattern continued over the course of a few weeks. Toni would produce work quickly and without proof, even though we talked about and shared proofs explicitly during our class discussions.

This came to a head on a classwork assignment about trapezoid properties. My major goal for the lesson was to help students understand how to use parallel lines and triangles to write proofs about quadrilaterals. I gave students a problem set including the question, “Is it always, sometimes or never true that the sum of the angles of a trapezoid is 360 degrees?”

I came over to Toni and saw that she had written “always” by it. I nudged her to offer an argument, and she wrote “Because all quadrilaterals sum up to 360 degrees.” I asked her how we knew that, and she wrote “y=180(n-2)” on her page. Eventually, with a bit more nudging, she wrote "alternate interior angles are supplementary."

During my initial instruction I had suggested that students try to use parallel lines and alternate interior angles and the decomposition into triangles to develop these trapezoid proofs. The day before, we had worked on a proof that triangle angles sum to 180, and a student had shared a proof using parallel lines. I tried to use questioning to push Toni in this direction, but even as were talking she was looking at other problems and patiently waiting for me to leave her alone.

In other words, my initial instruction failed.

Now, Skeptic, how would you have me react to this failure of initial instruction?
  • Explicit instruction in a whole-class setting had already failed, and it’s not hard to understand why. Toni was heavily invested in being especially good at math, and was heavily incentivized to avoid making a connection between corrections in instruction and her own work.
  • I could create a new task whose sole purpose was to focus on the need to justify our claims in geometry. This would suffer from the same issues as explicit instruction, though. A further issue: the new task would, by definition, have new intellectual demands that would distract from the old ideas that I wanted Toni to learn. Any new math would be something else for her to think about rather than laser-focusing her on her areas of improvement.
  • I could try conferencing one-on-one with her during class, but this had already shown itself to be problematic. Her status/mindset issues suffice to explain why this had failed. Toni has trouble yielding when in the presence of her friends and peers.
  • I couldn't meet with Toni outside of class. She didn't see herself as needing my help, and the logistics of arranging an out-of-class meeting are difficult for us.
  • What about simply giving feedback without time to improve her work? This feedback is easily forgotten and ignored, in general, and wouldn't have been taken to heart by Toni, who has shown herself to be especially unreflective when it comes to proof and argumentation.
I decided that the only course of action that had a chance of working was giving feedback to the whole-class and asking the entire class to improve their earlier work. This way, Toni wouldn’t be able to escape from the connection between my instruction and her own work. She wouldn’t have any other mathematical distractions -- any other problems for her to show her ability on by rushing on to them during instruction. Most importantly, since the entire class would be improving their work, she wouldn't feel as if her struggles were on display for others. Toni could have a chance to quietly make improvements without losing status in the eyes of friends.

Here's how I did it: I handed everyone’s papers back with no comments, to minimize everyone's ego-involvement. Then I posted on the board: “Is it always, sometimes, or never true that a kite can be divided into two congruent triangles?”

After discussing the problem and sharing proofs verbally, I told the class that I had read and enjoyed their work from yesterday, but had noticed that lots of them had room to improve their proofs. I said that proof-writing is new to a lot of us, and is a different skill than answer-getting in geometry. We can get better at both, I argued. (At this, Toni groaned.)

Then I shared three “sample” responses to the kite problem:

Not a proof. No reasons given

OK proof. Reasons given, but they're private reasons

Great proof. Reasons given that others can understand.

After giving this feedback, I said: "Pick one of your problems from yesterday, and write a nice, improved proof, like this third proof, on a new piece of paper."

And then...


OK hold on a sec. This is Skeptic again, and I know where this is going. "And after this, the look of understanding! a smile blooms on Toni's face! She laughs and says, 'Mr. Pershan, I didn't realize that I can do this!'"

Right. And from that day on, Toni's proofs were much improved, and her attitude in class was better, and then five years later she calls to tell you how important your class was to her.

Pardon me, but I'm skeptical. I don't know Toni. No one knows Toni. You know Toni, and for all we know you're making this up. 

You expect us to believe your "second drafts" idea based on your totally unverifiable story?




I don't expect anyone to believe me based on my word. You shouldn't. I'm probably not making this up, but I'm also not an objective observer of my own classroom. Further, I can't be sure that what I think caused Toni to improve actually caused her improvement.

Instead, inspect my thinking. I'm not claiming that asking Toni to improve her work caused her to learn how to write a proof. I'm claiming that this was the only sensible teaching decision to make in this situation. Is there a flaw in my instructional reasoning? Is there an alternative to classwork-improvement that I didn't consider? Do you think that one of the solutions I dismissed could have helped?

If my reasoning is sound, then the first half of my response to a skeptic (and Skeptic) goes like this: this is a type of situation where asking students to improve their work is the best teaching decision. When a student's struggles aren't even on his own radar, asking for a second-draft is often going to be the best course of action, in particular when that student is disposed not to see their own areas of improvement.

But the skeptic's gap remains: how do we know that asking for a second draft is a generally useful teaching move, and not just helpful in the specific scenario that I outlined above? 

The best I can personally do is share my hunches and speculations. But that's another post for another day.


I love your comments, and I have a special love for your skeptical comments. Here are some questions I'm thinking about after writing this post.
  1. Do you think that asking students to improve their work is generally helpful for learning? Why do you think so?
  2. In some ways, this was pretty cautiously argued. Is this sort of justification of teaching decisions necessary? 
  3. Should we believe the evidence that teachers report from their classroom? Would you have been convinced if I had just said "...and now Toni is writing amaaazzzing proofs"?
  4. Is there still room for the skeptic?

As it happens, Toni's proofs have been much better.

And for those playing at home, cross off "whole-class," "verbal" and "goal-setting" on your feedback Bingo card.

This is the third post in a series on feedback. To read the rest of the posts click here.

Saturday, November 8, 2014

Kids Learn From Second Drafts (2 of 10)

In this post, I'd like to argue that "giving feedback" is a lousy teaching concept. I'll suggest that instead of worrying about how to give effective feedback, we'd be better off thinking about how to help students improve their work in a second draft.

I've pointed out that there is significant, widespread disagreement within the teaching profession about the usefulness of feedback to learning. And I think that "feedback" only has itself to blame. It's a famously difficult concept to define, probably due to the convoluted route it took from its origins in electrical engineering through group dynamics, finally landing into the psychology of learning and then into popular usage. Along the way, "feedback" went from meaning something precise ("when the output of a system in turn becomes an input") to something vague ("when a person says a thing to another person about some thing that the first person did").

Because of the vagueness of the term, to tell a teacher "give some feedback" gives him practically no guidance. I think that more helpful advice would be to tell a teacher, "help the kids to improve their work," or "have them do a second draft of their classwork."

Consider a quick scenario. Suppose that you're teaching eleven 3rd Graders how to read bar graphs. You finish a first round of instruction and give them this bar graph and some questions to answer.

You collect their work, and read their responses in more detail. Their thinking is varied. Some ideas are mistakes, and (as always) there are aspects of their work that could be better. In particular...
  • Some students looked at the gap between 180 and 200 and concluded that there were only 20 non-walkers from Parks School.
  • In response to "How many students either bike or walk to Lincoln School?" some students wrote "60 and 40" instead of "100."
  • When prompted to explain some of the differences between these two schools, some kids stop short of conjecturing what the underlying differences between Parks and Lincoln might be.
A teacher who wants to help these kids by "giving feedback" might do any number of things. She might go through the questions one by one with students in whole-group. Or he might indicate right/wrong on the page and ask students to make corrections. Or she might make the corrections on the page for the student. Or he might ask students to check each others' work. 

You might start wondering, what are we trying to accomplish with this feedback? When does it lead to learning? When is it a waste of time?

Here's my motto: Kids learn from improving their work, and effective feedback is whatever it takes to make that improvement.

What I ended up doing with this 3rd Grade class was highlighting in blue something that I thought was really great in their work, and something in yellow that I thought they could improve. I handed back their work and let them work with partners on improving (and finishing) their assignment while I circulated and had conversations where I checked in.

In the course of things, a "20 non-walkers" student understood had a chance to think things through and improve their answer.

Students who didn't know how to explain the data had a chance to improve their work.

The feedback that we'll end up giving is going to vary drastically depending on the math, the students, and the teacher. I give written feedback, verbal feedback, whole-class feedback, individual feedback, small-group feedback, questions as feedback, observations as feedback, advice as feedback.

The only non-negotiable here is the goal. The goal is to help kids see ways that they can improve their work and then to give them a chance to do so.

At this point, a good skeptic might be doubting whether a student improving their work really leads to learning. Or whether creating a second draft is more effective than other forms of instructional activities, like directly telling or working on a task that's related to the first. These are good, important questions. 

In the next post in this series, I'll make the case that there are times when improving student work is the best instructional move available.

This is the second post in a series on feedback. To read the rest of the posts click here.

Tuesday, November 4, 2014

The Four Myths of Feedback (1 of 10)

Is this good feedback? Circling the areas of mistakes, highlighting areas of concern, debugging students' work?

Is this? Asking questions, explaining the mistake that a student made?

More puzzles:
  • Why do some teachers report that their students just crumple up their feedback, while others teachers swear by the feedback cycle?
  • Why do some teachers report giving written feedback to be inefficient and exhausting, while others find it manageable?
  • How can we bridge these huge gaps in teacher perceptions? Why hasn't research settled these questions for teachers already?
My hypothesis is that we're talking past each other. Do kids like feedback? Which kids? Is written feedback exhausting? Well, what sort of feedback are you talking about? 

So much of teaching is in the details. Unless we give these details in our writing about teaching we can hardly be sure what we're talking about. Without classroom evidence, discussions get very fuzzy, very quickly.

In this series of posts I'm going to use stories from my classes to argue for the viability of a certain kind of feedback. In particular, I have my aim set against four claims about feedback that I consider to be myths. 

Without further ado, here they are, your myths!

Four Myths of Feedback
  1. Oral feedback is always better than written feedback.
  2. When it comes to feedback, the more the better!
  3. When it comes to feedback, the sooner the better!
  4. Feedback is all about helping students understand the mistakes they've made.
Don't agree? I'm not surprised! These statements have been presented entirely without context or grounding in any classroom. My job over the next 9 posts in this series is to put flesh on the bone of these claims with some believable evidence from my classroom.

You have two jobs. First, to be productively skeptical. I'm going to be providing you with enough detail that you'll be able to disagree with my interpretations of the classroom. As far as I can tell, this is rare for a writer about teaching to do, and I'm looking forward to our disagreements.

Your second job is to think of stories from your own teaching that might add to the feedback picture. My classroom has its own particular constraints. So does your's. We'll learn a bunch from the collage that emerges from the volley of classroom stories.

This is the first post in a series on feedback. Once they're all written I'll link 'em up here at the bottom of the post. In the fuuuutre.

Update: Welcome to the future! Here's the whole series. (link)

Sunday, November 2, 2014

Focusing On Feedback

I want to try a bit of a writing experiment. The next ten posts that I write will be about giving feedback. The plan is to stray away from abstractions and research summaries. Instead, I want to make the case for the decisions that I'm making in class through stories and analysis.

So, stay tuned!